Superheated steam is steam obtained by further heating steam that is at 100° C. For example, a superheated-steam oven cooks foodstuffs by directly blowing superheated steam to the foodstuffs so as to bake them. The food-cooking apparatus disclosed in JP-A-2004-24322 connects multiple steam-heating pipes, into each of which a heater is inserted, with short non-heating pipes. The food-cooking apparatus disclosed in that prior-art document has the following characteristics: (1) because there is only a small space in the food-cooking apparatus, it is difficult to weld the short non-heating pipes onto the steam-heating pipes; (2) in order to connect the short non-heating pipes to the steam-heating pipes, holes must be drilled in the steam-heating pipes; and (3) the food-cooking apparatus is generally box-shaped, having a large width and a large depth despite having a low height. Therefore, if the food-cooking apparatus (i.e., superheated-steam generator) is to be formed into a cylindrical shape like a device, the welding of the short non-heating pipes onto the steam-heating pipe is very difficult.